Regular Article
On Spectral Cantor Measures

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Abstract

A probability measure in Rd is called a spectral measure if it has an orthonormal basis consisting of exponentials. In this paper, we study spectral Cantor measures. We establish a large class of such measures, and give a necessary and sufficient condition on the spectrum of a spectral Cantor measure. These results extend the studies by Jorgensen and Pedersen (J. Anal. Math.75 (1998), 185–228) and Strichartz (J. D'Analyse Math.81 (2000), 209–238).

Keywords

Spectral measure
Cantor measure
IFS
Ruelle operator.

Cited by (0)

Communicated byL. Gross

f1

[email protected]

f2

[email protected]

1

To whom correspondence should be addressed.

2

Supported in part by the National Science Fundation Grant DMS 0070586.